Relationships Between Lung Structure and Function

The evolutionary “decision” to conduct gas exchange by passive diffusion (rather than by energy-requiring active transport) was a profound one that dictated the basic structure of the lungs. The laws of diffusion show that diffusive mass transfer rates are directly proportional to the surface area available for diffusion and are inversely proportional to the distance the molecule must diffuse. The fundamental unit of structure in the lung is the alveolus, small and roughly spherical in shape, with an average radius of 150 micrometers (µm). There are about 300 million alveoli in the human lung. Each is supplied with air that must pass through the branching bronchial tree (conducting airways). The wall of each alveolus, shared by adjacent alveoli, is packed with capillaries. The tissue separating alveolar gas from the blood in the capillaries consists of the capillary endothelium, interstitial matrix, alveolar epithelium, and a thin layer of fluid. The entire wall is less than 0.5 µm in thickness.

These dimensions imply a total alveolar surface area of about 80 m², yet a gas volume of only 4 L (small enough to fit within the chest cavity). Thus, the actual lung can conduct diffusive exchange efficiently because of the large surface area and small diffusion distance. By contrast, if the lungs consisted of just a single large sphere of the same 4-L volume, its surface area would be only m² (640-fold less). Moreover, if the same mass of 0.5-µm-thick alveolar wall tissue covering all 300 million alveoli were spread around this one sphere, its thickness would be over 300 µm, also about 600 times greater than in the actual lung. Because diffusion rates depend on the ratio of area to thickness, the real lung is about 640 × 600, or 400,000 times better at diffusive transport than would be a single sphere of the same volume and mass. The message is that by dividing up the lung into a very large number of very small structures, diffusion becomes a feasible and energy-efficient method of gas exchange, circumventing the need for active transport.

This picture of the lungs is similar in some ways to a bunch of grapes in which each grape is an alveolus, the skin is the alveolar wall (containing the capillaries) and the pulp inside is the alveolar air space. The stalks connecting each grape to its cluster depict the conducting airways and blood vessels. A major shortcoming to the grape analogy, however, is that each grape in a bunch is physically detached from all others in the bunch. However, all alveoli are connected, sharing common alveolar walls, much like the cells of a honeycomb. This connectivity means that the alveoli are mechanically interdependent—they pull on each other, forming a self-stabilizing three-dimensional network.

Challenges to Lung Function Caused by its Structure

Lung structure may be optimized for diffusion, but it results in several potentially life-threatening challenges:

In sum, many life-threatening challenges may be associated with a lung built for diffusion, affecting the airways, alveoli, and blood vessels. In the normal lung, defenses against them are satisfactory, but in lung disease, they often are inadequate, with sometimes fatal outcomes.

Gas Exchange in the Homogeneous Lung: Ventilation, Diffusion, and Perfusion

Because gas exchange obeys mass conservation rules and occurs by passive diffusion, the exchange of gases can be understood and predicted quite accurately in a quantitative sense. In fact, quantitative discussion is essential to understanding of not just the principles but also the clinically very important differences in behavior of O₂, CO₂, and other gases. It is best to start with a perfectly homogeneous lung—one in which every alveolus is assumed to be identical and to receive an equal share of both ventilation and blood flow. Although an obvious oversimplification, this assumption allows the establishment of the basic principles, which can then be readily applied to lungs in which differences in ventilation and blood flow exist among alveoli.

Ventilation

For ventilation, mass conservation means that the amount of O₂ diffusing into the pulmonary capillary blood from the alveolar gas in a given period (say, 1 minute—i.e., ) can be expressed as the difference between how much O₂ was inhaled and how much was exhaled (over that minute). This relation holds because inhaled O₂ has only two fates—diffusing into the blood or being exhaled. The amount inhaled is the product of minute ventilation and the concentration of O₂ in inhaled air; the amount exhaled is the product of minute ventilation and the concentration of O₂ in the exhaled gas. Because O₂ concentration is constantly changing during the course of an exhalation, it is appropriate to use the mean concentration over exhalation. Minute ventilation is the product of the volume of each breath (L/breath) and the frequency of breathing (breaths/minute). Although the volumes inhaled and exhaled might be expected to be the same (or the lungs would either blow up or collapse), exhaled volume usually is 1% less than that inhaled because the amount of O₂ absorbed into the blood is a little more than the amount of CO₂ eliminated from the blood. This small difference can be neglected in most circumstances, as is the case in the following discussion. The mass conservation equation that then describes O₂ uptake as a function of ventilation is

where is the volume of O₂ taken up into the blood per minute, and is the minute ventilation, both expressed in L/minute. FIO₂ and FEO₂ are, respectively, the inhaled and exhaled mean O₂ fractional concentrations. commonly is about 7 L/minute. Because about 21 of every 100 molecules in air are O₂ molecules (the rest being mostly nitrogen), FIO₂ is 0.21. FE_O2 at rest is about 0.17; this difference shows that is about 0.3 L/minute. Because the conducting airways that feed the alveoli do not exchange O₂ or CO₂, it has become conventional to subtract the volume of gas left in the conducting airways each breath—the so-called anatomic dead space—from the total breath volume before multiplying by respiratory frequency to calculate ventilation, resulting in a variable known as alveolar ventilation (). Equation 1 then becomes

where FAO₂ is now the mean alveolar O₂ concentration. FAO₂ is higher than FEO₂ because the latter combines the inhaled air from the dead space with the alveolar gas, which is lower because of O₂ transfer into the blood.

The tendency is to use partial pressure (PI_O2, inhaled; PAO₂, alveolar) rather than fractional concentration (FI_O2, FAO₂) in describing these relationships: From Dalton’s law of partial pressure, PO₂ = FO₂ × (barometric pressure − water vapor pressure). Allowing for proper units, Equation 2 can then be rewritten as

is now expressed in mL/minute, in L/minute, and P in mm Hg.

is the whole-body metabolic rate and as such is dictated by the body tissues, not the lungs. Because PI_O2 is a constant, Equation 2 can be used to demonstrate the dependence of alveolar PO₂ on alveolar ventilation for a given value of (Figure 5-1). The same concepts apply to CO₂, for which it is simpler, because CO₂ is essentially absent from inhaled air. The corresponding equation is

Figure 5-1 Relationship between alveolar PO₂/PCO₂ and alveolar ventilation when metabolic rate is held constant. Dashed lines indicate normal ventilation, PO₂ and PCO₂. Note that as ventilation is reduced, even moderately, PO₂ falls sharply and PCO₂ rises similarly.

How ventilation affects PACO₂ also is shown in Figure 5-1. It is evident that a relatively small reduction in ventilation will reduce PAO₂ and increase PACO₂—both substantially.

Dividing Equation 4 by Equation 3 gives

which can be rearranged into what is called the alveolar gas equation:

This equation, which relates alveolar PO₂ to alveolar PCO₂ for a given respiratory exchange ratio R, is very useful at the bedside, as discussed later on.

Diffusion

The laws of diffusion dictate that the rate at which a gas diffuses between two points is the product of the diffusion coefficient for the gas and the partial pressure difference between the two points. In the lungs, the diffusion coefficient, measured as the diffusing capacity, is determined by surface area and distance of the diffusion pathway (see earlier). When a red cell leaves the pulmonary arteries and enters the pulmonary capillary, it arrives with a reduced level of O₂, because the tissues visited by that red cell took O₂ from the red cell for the tissue’s metabolic needs. The PO₂ in the red cell in this blood commonly is about 40 mm Hg. Alveolar PO₂, on the other hand, usually is about 100 mm Hg. The large PO₂ difference (“driving gradient”) of 60 mm Hg leads to rapid diffusion of O₂ from the alveolar gas into the capillary blood. Consequently, however, the blood PO₂ increases, reducing the driving gradient, and O₂ diffusion slows down as the red cell progresses along the lung capillary network. With modeling of this process, again using mass conservation principles, PO₂ is seen to rise approximately exponentially as the red cell moves along the lung capillary until PO₂ in the red cell has reached the alveolar value, indicating that diffusion equilibration has occurred. This process is shown in Figure 5-2. Note that for O₂, equilibration occurred in about 0.25 second. On average, each red cell takes about 0.75 second to move through the alveolar capillary system, so that diffusion equilibration is complete already a third of the way along the capillary, and thus well before its end. As might be expected, during exercise, time available for a red cell to pick up O₂ in the lung is reduced, because blood flow rate is increased, and at very high exercise intensity, there may not be sufficient time for PO₂ in the red cell to reach the alveolar value. Accordingly, PO₂ in the systemic arterial blood will be lower than that in the alveolus—a situation referred to as hypoxemia caused by diffusion limitation. This effect is seen commonly in exceptional athletes exercising heavily at sea level, and in all subjects exercising at altitude.

Figure 5-2 A, Rate of rise in gas partial pressure along the capillary. Inert gases equilibrate very rapidly, and O₂ more slowly, but CO fails to equilibrate. B, Rate of fall in CO₂ partial pressure along the capillary. CO₂ equilibrates about twice as rapidly as does O₂.

While CO₂ moves from blood to gas, the principle is the same as for O₂. Here, the red cell enters the alveolar capillary with a high PCO₂ (because of addition of waste CO₂ from tissues visited by the red cell), whereas alveolar PCO₂ is lower. Thus, diffusion will move CO₂ from red cell to alveolar gas, and red cell PCO₂ will fall toward the alveolar value in mirror image to the rise in PO₂ described earlier (see Figure 5-2). The speed of equilibration for CO₂ is about twice that for O₂, so it takes about half the time to reach equilibration. In practice, CO₂ is never diffusion-limited. Gases carried in blood only in physical solution (i.e., inert and anesthetic gases) equilibrate even faster—about 10 times as quickly as for O₂ (see Figure 5-2). This rule holds true for gases of any solubility.

In the remainder of this chapter, diffusion equilibration is assumed to be complete for all gases discussed. What this means is that the alveolar (A) and end-of-the-capillary (ec) PO₂ values are the same for any one gas. Thus, for O₂, PAO₂ = PecO₂.

Perfusion

From the preceding, it is clear that O₂ brought to the alveoli by ventilation then diffuses into the flowing blood in lung capillaries. O₂ uptake into the blood can be described using mass conservation principles, just as for ventilation. Thus, the amount of O₂ taken up into the flowing blood per minute () is the amount of O₂ in the blood leaving the lungs each minute heading for the left atrium, minus the amount that had entered the lungs in the pulmonary arterial blood. These amounts are the product of the concentration of O₂ in each site and the blood flow rate. If CecO₂ is the concentration of O₂ in the end-capillary blood, CvO₂ is the concentration of O₂ in the capillary blood as it enters the lung capillaries, and is the blood flow rate through the lungs, mass conservation gives

Because O₂ concentration in end-capillary blood is virtually unchanged between the end of the capillary and the systemic arterial circulation, end-capillary O₂ concentration can be replaced with arterial CaO₂, giving

This relationship is known as the Fick principle. For CO₂, the corresponding equation is

Gas Exchange

Focusing on O₂, Equations 3 and 8 should now be considered together. They both embody mass conservation but express it differently, with Equation 3 reflecting alveolar loss of O₂ into blood and Equation 8, red cell gain of O₂ into blood. Figure 5-3 shows how, for given constant values of and , and for designated values of inspired PO₂ (PI_O2) and inflowing pulmonary arterial O₂ concentration (CvO₂), would have to vary with alveolar PO₂ (to satisfy both these equations) when determined by each of the two equations independently. Because each molecule of O₂ that leaves the alveolus by crossing the blood gas barrier appears in the capillary blood, the calculated from the two equations must be the same—again, conservation of mass. Thus, only a single value of PAO₂ can exist—that at the point of intersection of the two relationships in Figure 5-3. If the calculations in Figure 5-3 were repeated for different values of , and thus (in this example, keeping the same), the lines and their point of intersection would change as in Figure 5-4. This figure shows that alveolar PO₂ (x axis) and the amount of O₂ that can be taken up (, y axis) both depend on and . Commonly, Equations 3 and 8 are combined, because must be the same when calculated from either equation. This yields the ventilation-perfusion equation:

Figure 5-3 The two mass conservation equations for calculating O₂ transfer rate (): one as a function of ventilation (, straight line) and the other based on blood flow (, curved line), as alveolar PO₂ (PAO₂) varies. Inspired and mixed venous O₂ levels are held constant, as are and . The point of intersection (open circle) is the only combination of and PAO₂ for which mass of O₂ is conserved and indicates the PAO₂ that must exist for the given values of and .

Figure 5-4 Same analysis as in Figure 5-3, with the four straight lines reflecting four values of ventilation, , but only one value of blood flow, (and thus yielding four values of their ratio, ). PAO₂ increases with , as shown by the four filled circles.

or

and the equivalent for CO₂:

These equations say that it is the ratio of to that determines the alveolar PO₂ and PCO₂ in any region of the lungs.

Figure 5-5 shows how alveolar PO₂ and PCO₂ vary with when inspired PO₂ is that of room air and the pulmonary arterial (mixed venous) PO₂ is normal (i.e., 40 mm Hg). Important conclusions to be drawn from this figure are that as falls, PO₂ falls, approaching the mixed venous value at low values, and conversely, PCO₂ rises. Also, as rises, PO₂ approaches the inspired value, while PCO₂ falls. The dashed lines show that at the normal value for the ratio of about 1, PO₂ is about 100 mm Hg, and PCO₂ is about 40 mm Hg.

Figure 5-5 How alveolar PO₂ (and PCO₂) vary with ventilation-perfusion ratio (), based on the analysis of Figures 5-3 and 5-4. Dashed lines show normal values for a of 1. Normal conditions are assumed: inspired PO₂ = 150 mm Hg, PCO₂ = 0 mm Hg, mixed venous PO₂ = 40 mm Hg, PCO₂ = 45 mm Hg. PAO₂ and PACO₂ approach mixed venous values as approaches zero and inspired values as approaches infinity.

Although the behavior of the two gases is qualitatively similar (even if opposite in direction), their quantitative behaviors are different. Most of the variance in PO₂ occurs over the range 0.3 to 3, whereas for CO₂, most of its change is seen in the range 2 to 20, almost a decade higher. The gases obey the very same conservation of mass rules in their exchange, so their quantitative differences are due to differences in their transport properties in blood.

Ventilation-Perfusion Inequality and Gas Exchange

The preceding analysis accounts for gas exchange in the intact, homogeneous lung, in which a single value is taken for (equal to the ratio of total alveolar ventilation to total pulmonary blood flow). In real life, not all alveoli enjoy the same to ratio. In fact, even in healthy young humans there is about a 10-fold difference between the lowest and highest values, from a low of about 0.3 to a high of about 3. This difference is due to both gravitational influences (higher in nondependent than in dependent regions) and nongravitational factors such as variation in length and diameter of airways and blood vessels. Alveoli with different ratios are connected in parallel: Mixed venous blood reaches them all, and then the end-capillary blood from each flows into the pulmonary veins, much like tributaries joining a river. In lung diseases, variation in (also called inequality) can be extreme and even fatal. Thus, it is essential to consider how such inequality affects the ability of the lungs to take up O₂ and eliminate CO₂.

This analysis can be done by comparing a homogeneous lung to one with the simplest degree of inequality—a lung imagined to have two “alveoli” of different ratios. This schema is illustrated in Figure 5-6. In the left panel, the homogeneous case, with a total ventilation of 6 L/minute and a total blood flow also of 6 L/minute, both equally divided between two identical “alveoli,” PO₂ and PCO₂ values can be read off Figure 5-5 for the resulting ratio of 1.0. In the case of inequality, the example in the right panel shows the effect of severe but incomplete airway obstruction, causing 90% reduction in ventilation of the left “alveolus,” with corresponding redistribution of ventilation to the right “alveolus” (that is, total ventilation and blood flow are assumed to be unaltered by the airway obstruction). The PO₂ values are again read from Figure 5-5 and are now 45 and 120 mm Hg, respectively. As the two “alveoli” exhale, their gas streams mix in proportion to the relative gas flow rates, resulting in a mixed exhaled PO₂ of 116 mm Hg. Similarly, the blood leaving each “alveolus” has the same PO₂ as in the respective alveolar gas, as shown, and these two blood streams mix again in proportion to their blood flows. Here the computation is performed using the concentrations, not partial pressures, and when this is done, the mixed arterial PO₂ is reduced to only 60 mm Hg.

Figure 5-6 A two-compartment representation of ventilation-perfusion distribution showing how maldistribution interferes with gas exchange. Left, The homogeneous example in which each compartment having the same also must have the same PAO₂. When exhaled air and end-capillary blood from the two compartments mix, the mixed exhaled gas and mixed arterial blood have the same PO₂. Right, Effects of altered distribution of ventilation due to airway obstruction on the left side, reducing ventilation and thus each 10-fold. Mixed exhaled PO₂ is higher and mixed arterial PO₂ is lower than in the homogeneous case, and total O₂ uptake is reduced—all as total ventilation and total blood flow are held constant.

Thus, what this simple calculation shows is that when the ratio is not everywhere the same, gas exchange suffers: Arterial PO₂ falls, and the amount of O₂ taken up by the whole lung also falls (which can be deduced from the increase in mixed exhaled PO₂, which means that because more O₂ was exhaled, less O₂ was transferred into the blood).

The same occurs for PCO₂, but in the opposite direction: inequality increases arterial PCO₂, reduces mixed exhaled PCO₂, and thus also reduces the amount of CO₂ eliminated. Figure 5-7 shows the values for CO₂ for the same case as in Figure 5-6. What is seen, however, is a quantitatively larger negative effect on O₂ than on CO₂, in terms of both the arterial partial pressures and total amounts of gas transferred.

Figure 5-7 Corresponding calculations for CO₂ in the same model as in Figure 5-6, right. CO₂ output is impaired, whereas arterial PCO₂ is increased and exhaled PCO₂ is decreased, although the changes are less than for O₂.

That O₂ is more affected than CO₂ in this instance reflects the nature of the example: The obstructed “alveolus” has a very low ratio. With modeling of exactly the same problem but this time reducing blood flow in one “alveolus” by 90%, rather than reducing ventilation as in Figures 5-6 and 5-7, inequality would still be present and both gases would be affected, but because the abnormal “alveolus” has a high and not low ratio, the quantitative effects are different: CO₂ is affected more than is O₂.

This result points out that the effects of inequality are always to impair gas exchange for all gases, but the degree to which any one gas is affected depends on the exact pattern of distribution of ventilation and blood flow. The basic reason why O₂ and CO₂ are differently affected in any given pattern is found in the differences in their dissociation curves in blood. That for O₂ is quite nonlinear; that for CO₂ is almost linear and also is much steeper. In sum, O₂ is affected more when low regions dominate; CO₂ is more affected when high regions dominate.

Shunt

Shunt refers to blood that crosses from the right to the left side of the heart without encountering any alveolar gas. This pathophysiologic entity can be due to ventricular or atrial septal defects and other intracardiac anomalies, or to lung lesions such as complete airway obstruction, atelectasis, pneumothorax, pulmonary edema, pneumonic consolidation, and large arteriovenous intrapulmonary vascular malformations. Referring back to Figure 5-6, which illustrates partial airway obstruction, a shunt could be modeled by assigning zero ventilation to the left “alveolus” and all the ventilation to the right side. The effects would be slightly more severe than those illustrated for partial obstruction, but the point is that a shunt can be thought of as an extreme of inequality: a region with = 0, because ventilation is absent.

There is, however, a special feature of shunt that merits discussion: response to inhalation of 100% O₂. When inequality is present, and 100% O₂ is inhaled, all alveolar nitrogen that had been present in the lungs of a subject breathing room air will eventually wash out, and the only gases in the alveoli will be O₂ and CO₂. PO₂ in all alveoli will be above about 600 mm Hg, no matter what the ratio is for each alveolus. Accordingly, on 100% O₂, a lung with inequality will exchange O₂ normally. In the presence of shunt, however, the shunted blood is never exposed to 100% O₂, and its PO₂ remains low (at PO₂ in the inflowing pulmonary arterial blood). This, using the same principles as in Figure 5-6, causes the mixed arterial PO₂ to be abnormally low even as 100% O₂ is inhaled.

The Four Causes of Hypoxemia

As characterized in the preceding discussion, arterial hypoxemia (defined as a subnormal value of arterial PO₂) has four different causes:

The alveolar gas equation derived earlier (Equation 6) is useful in separating hypoxemia from these various insults: For hypoventilation alone, the equation predicts exactly how much arterial PO₂ will fall for any given increase in arterial PCO₂, because the alveolar PO₂ and the arterial PO₂ remain equal. However, as shown in Figure 5-6, for inequality, the exhaled alveolar PO₂ increases while the arterial PO₂ falls. Equation 6 is used to compute alveolar PO₂ by inserting arterial PCO₂ into the equation, and when this is done and the arterial PO₂ is subtracted from it, one has what is called the alveolar-arterial PO₂ difference PO₂(A−a). The typical patterns of arterial PO₂, PCO₂, and PO₂(A−a) are illustrated in Table 5-1 for each cause of hypoxemia, together with the response to 100% O₂ breathing mentioned earlier. In Table 5-1, it is specifically assumed that the body has not reacted to the hypoxemia by any of the compensatory mechanisms normally available to it, as discussed next. In life, such compensatory reactions are the rule, unless special circumstances such as trauma, heart disease, or narcotic overdose also are present.

Compensatory Mechanisms

When hypoxemia develops for any reason, three principal compensatory mechanisms are invoked:

These mechanisms act to restore the mass flow of O₂ and CO₂ across the lungs, returning and to levels necessary to sustain tissue metabolism. Failure to invoke these mechanisms leads to tissue death and can be fatal.

Clinical Assessment of Gas Exchange Based on Physiologic Principles

The entire preceding discussion has provided a physiologic basis for clinical tools to assess pulmonary gas exchange. All of these tools are based on measurement of PO₂ and PCO₂ in an arterial blood sample. Because measuring the entire distribution of ventilation and of blood flow is complex and time-consuming, several simplified methods of gas exchange analysis have been proposed.

Alveolar-Arterial PO₂ Difference: PO₂(A−a)

As noted earlier, Equation 6, derived previously, is called the alveolar gas equation.

If an arterial blood gas sample is taken, arterial PO₂ (PaO₂) and arterial PCO₂ (PaCO₂) are available. PaO₂ as measured can then be subtracted from PAO₂ as calculated from Equation 6, to get PO₂(A−a):

In a perfect lung, PO₂(A−a) would be zero. In a normal lung in a young, healthy subject, PO₂(A−a) is about 4 to 10 mm Hg. It can increase to as much as 60 mm Hg in severe lung disease.

Shunt: s/t

Even if the lung is complex in disease, it can always be modeled as consisting of two “compartments”: one normal and one completely unventilated (i.e., in which all the blood flow is shunted). As described previously, shunted blood takes on no O₂, so that the blood leaving has the same low O₂ level as that entering in the mixed venous blood. The objective is to calculate that fraction of the cardiac output (/t) necessary to flow through the “shunt” compartment to explain the measured arterial PO₂. This calculation is done using the shunt equation, as follows:

This is a conservation of mass or mixing equation that states that the arterial O₂ concentration (CaO₂) is the blood flow–weighted average of the concentrations of O₂ coming from the shunt (, shunt flow; CvO₂, mixed venous O₂ concentration) and the normal compartment (t − , nonshunt blood flow; CecO₂, end-capillary O₂ concentration). t is total blood flow, or cardiac output. Equation 13 can be rearranged as follows:

This is called the shunt equation. To use it, CecO₂ is calculated using the oxygen-hemoglobin dissociation curve, and the PAO₂ as calculated from Equation 6; CaO₂ is determined from an arterial blood gas sample, and CvO₂ is either assumed or measured from a mixed venous blood sample. If CvO₂ is assumed to have a specific value, the calculated value of shunt fraction (s/t) is only as accurate as the assumed value of CvO₂.

If data for this equation were collected with the patient breathing 100% O₂, a true value of shunt would be found. Recall that, as explained previously, when the subject is breathing 100% O₂, even low alveoli have very high PAO₂ values, exceeding 600 mm Hg, and thus would not contribute to a discernible reduction in CaO₂, because the alveolar blood is fully O₂-saturated. If, however, the data came from a patient breathing less than 100% O₂, the value for /t would in general be larger, because when less than pure O₂ is breathed, areas of low ventilation-perfusion ratio contribute numerically to what appears as /t, because they show less than full O₂ saturation of hemoglobin.

Physiologic Dead Space: Vd/Vt

In a conceptual mirror-image formulation, total dead space can be calculated as another parameter of abnormal gas exchange. Conventionally, CO₂ has been used as the marker gas for this, not O₂. The basis is again conservation of mass, and the concept makes use of another two-compartment model. This time, while one compartment remains normal, the other is given an infinitely high ratio of —that is, it is ventilated ( > 0) but unperfused ( = 0). No gas exchange occurs because there is no blood flow. This compartment therefore wastes any ventilation it gets. Its alveolar PCO₂ is thus that of inspired gas, namely, zero. The objective is to explain the PCO₂ in mixed exhaled gas (PECO₂) as a ventilation-weighted average of the PCO₂ coming from each compartment—alveolar PCO₂ (PACO₂) from the normal compartment and zero from the dead space compartment. The mass conservation equation parallels that for shunt, as follows:

Here f is respiratory frequency, Vd is the volume of air inhaled per breath by the unperfused compartment, and Vt is total inhaled volume of air per breath. Rearranging this equation gives

Usually, alveolar PCO₂ (PACO₂) is replaced by arterial PCO₂ (PaCO₂) from an arterial blood sample, to arrive at

This dead space equation needs as input arterial PCO₂ as well as PCO₂ measured in mixed exhaled gas.

The foregoing discussion makes it clear that taking an arterial blood sample is critical for estimating all three parameters of gas exchange. For accurate results, an arterial blood sample is not sufficient. Mixed exhaled gas is required to determine R () in Equation 12 and for measuring mixed exhaled PCO₂ (PECO₂) as used in Equation 17. Moreover, Equation 14 requires an estimate of mixed venous O₂ concentration.

Buffering

When blood is examined, several weak acids and bases are present in solution in plasma, red cells, or both. The major concept here is that they are all in chemical equilibrium with the existing [H⁺]. Should the concentration of H⁺ ions (i.e., protons) increase for any reason (that is, should acidosis develop), positively charged protons can react with the negatively charged ionic form of the weak acid to form the combined, nonionic species. In this way, protons are removed from solution, thus raising the pH back toward normal. This sequence is evident when the chemical equation for this process is displayed:

(18)

The ionic form of the weak acid A (i.e., A⁻) combines with a proton (H⁺) to form the associated nonionic form HA, thus reducing free [H⁺] and thereby raising pH.

Should the opposite condition exist—a reduction in free [H⁺] (known as alkalosis), the reaction shown in Equation 18 can run from right to left, thereby increasing H⁺ ion levels and lowering pH back toward normal.

Important buffers in blood include plasma proteins, especially albumin, phosphate ions, and, inside the red cell, hemoglobin. These buffers form the body’s first line of defense against an alteration in pH. They are immediately available and work instantly. Once deployed, however, they can be of little further use until new molecules are synthesized. Thus, they are of limited long-term value for modulating acid-base disturbances and have limited quantitative effect.

The Kidneys

The kidneys can retain or excrete H⁺ and bicarbonate ions (HCO₃⁻) to preserve their levels in the blood and thus play a major role in controlling pH changes arising from acid-base disturbances. The details of renal function are beyond the scope of this discussion, and further information is available in any of several texts on the subject.

Two important aspects of the renal contribution to acid-base disturbances are as follows: First, the kidneys are slow to react noticeably to an alteration in pH. Somewhat akin to a freight train starting from a dead stop, renal action may begin as soon as pH is changed, but it takes hours to “get up to speed” and affect pH. Second, just as normal kidneys can play a major homeostatic role in restoring pH toward normal, when renal disease develops, the ability to excrete a normally acid urine may be compromised, resulting in accumulation of H⁺ ions, with consequent development of acidosis. The kidneys can therefore be a cause of acidosis when they themselves are abnormal, owing to failure of H⁺-excreting mechanisms that are invoked to deal with excess H⁺ in normal kidneys.

The Lungs

Just as the kidneys can counteract either an acidosis or an alkalosis, the lungs have the ability to do likewise. The lungs contribute to regulation of blood pH through changes in PCO₂ brought about by changes in ventilation. In sum, an increase in [H⁺] in the blood stimulates both central (ventral medullary) and peripheral (carotid body) chemoreceptors, which send neural signals to the respiratory control areas of the brain, which in turn direct the respiratory muscles to produce an increase in ventilation, thereby decreasing PCO₂ (refer to Equation 4). A decrease in [H⁺] does the opposite. This effect is achieved through the buffering principle, as described, with carbonic acid (H₂CO₃) as the weak acid, as follows. The reaction is greatly accelerated by carbonic anhydrase:

(19)

Thus, if acidosis develops, the entire reaction proceeds rightward, removing H⁺ ions, raising pH, and producing more CO₂ that can (usually) be easily eliminated by a (usually) modest increase in ventilation. Conversely, should alkalosis develop, the reaction proceeds leftward, liberating H⁺ ions to restore pH. The source of the CO₂ necessary to “feed” this backward reaction is a reduction in ventilation. In sum, changes in ventilation affect changes in PCO₂, which then cause the chemical reaction in Equation 19 to proceed rightward when there is acidosis (increased ventilation and lowering PCO₂) or leftward when there is alkalosis (lowering ventilation and raising PCO₂).

By writing the equilibrium version of Equation 19, the concentrations of H⁺, HCO₃⁻, and CO₂ can be related as follows:

(20)

or

where 0.03 is the solubility of CO₂ in plasma (water) in mmoles per liter per mm Hg unit. Taking logarithms of equation 21 and rearranging K and [H⁺] gives:

or

where pK is the negative logarithm of the equilibrium constant for the reaction in Equation 19 and equals 6.1. This equation is known as the Henderson-Hasselbalch equation and is widely used in describing acid-base disturbances. As can be seen, it relates pH to [HCO₃⁻] and PCO₂.

Because this equation contains three variables, their relationship should be expressed in three dimensions, which is difficult. Several ways of working with the equation to surmount this problem have been devised, and they are in essence graphical. Perhaps the most intuitive and widely used is the Davenport diagram, which plots [HCO₃⁻] on the ordinate and pH on the abscissa and uses isopleths of PCO₂ to allow consideration of variation in that variable. For example, if PCO₂ is held constant at its normal value of 40 mm Hg, the equation simplifies to

(24)

In this way, the value of [HCO₃⁻] for any given pH can be calculated, forming a single line on which each point satisfies Equation 24 for the same value of PCO₂—in this example, 40 mm Hg. Figure 5-8 shows this line on a Davenport diagram for a PCO₂ of 40 mm Hg and also for several other fixed PCO₂ values, as indicated. This set of PCO₂ isopleths then forms the framework for considering acid-base relationships, both normal and abnormal. The value in normal arterial blood is shown in this figure by the solid circle located at PCO₂ of 40 mm Hg, pH of 7.40, and [HCO₃⁻] of 24 mmol/L.

Figure 5-8 The Davenport diagram: Representation of the Henderson-Hasselbalch equation relating pH, [HCO₃⁻], and PCO₂. Each curved line shows the unique relationship between [HCO₃⁻] and pH for each single value of PCO₂ shown on the graph. The filled circle is the point corresponding to normal arterial blood.

Figure 5-9 plots as a series of solid circles the relationship between pH and [HCO₃⁻] when the same normal blood sample is exposed to and equilibrated with gases of different PCO₂ values (one at a time), after which pH and [HCO₃⁻] are measured. From Equation 23, the Henderson-Hasselbalch equation, it is evident that as the applied PCO₂ is raised above normal, pH must fall to below normal, and as PCO₂ falls below normal, pH rises above normal, as shown. The pH/[HCO₃⁻] relationship turns out to be almost straight, as the figure indicates. The steeper the line, the less is the change in pH for a given PCO₂. That is, the steeper the line, the more effectively [H⁺] is kept from changing. Because these results pertain to a single blood sample in vitro, no renal intervention is possible, and the line can be said to represent the buffering ability of the blood sample. Indeed, it is called the blood buffer line. The higher the plasma and red cell buffer levels, the steeper will be the buffer line.

Figure 5-9 The blood buffer line on the Davenport diagram. It is the line relating pH to [HCO₃⁻] as PCO₂ is varied in a given blood sample. See text for details.

Use of the Davenport diagram to describe acid-base disturbances is illustrated in Figures 5-10 through 5-13. Each figure depicts the consequences of one of the four possible types of acid-base disturbance—respiratory acidosis, respiratory alkalosis, metabolic acidosis, and metabolic alkalosis. In each, the CO₂ isopleths and normal blood buffer line are shown, along with the normal point, N. These diagrams often are very useful at the bedside because they allow the caregiver to visually assess, diagnose, understand, and quantify the sometimes complex acid-base states encountered in clinical practice.

Figure 5-10 The Davenport diagram for respiratory acidosis. An acute increase in PCO₂ moves blood pH from the normal position (N) to point A—that is, movement up the normal blood buffer line. Over several hours to days, renal compensation slowly restores pH through HCO₃⁻ retention, moving blood to point C.

Figure 5-11 The Davenport diagram for respiratory alkalosis. An acute decrease in PCO₂ moves blood pH from the normal position (N) to point A—that is, down the normal blood buffer line. Over several hours to days, renal compensation slowly restores pH through HCO₃⁻ excretion, moving blood to point C.

Figure 5-12 The Davenport diagram for metabolic acidosis. An acute increase in [H⁺] moves blood pH from the normal position (N) to point A—that is, down the line for normal PCO₂. Over seconds to minutes, ventilatory compensation quickly restores pH through hyperventilation, thereby reducing PCO₂, and moving blood to point C.

Figure 5-13 The Davenport diagram for metabolic alkalosis. An acute decrease in [H⁺] moves blood pH from the normal position (N) to point A—that is, up the line for normal PCO₂. Over seconds to minutes, ventilatory compensation quickly restores pH through hypoventilation, thereby increasing PCO₂, and moving blood to point C.

Figure 5-10 presents a Davenport diagram for respiratory acidosis. As the name implies, it is the result of insufficient ventilation to keep PCO₂ normal at 40 mm Hg for the given rate of metabolic production of CO₂. It is the necessary consequence of mass conservation as expressed in Equation 4. From the Henderson-Hasselbalch equation, a rise in PCO₂ due to insufficient ventilation causes a fall in pH. When changes in ventilation or metabolic rate occur rapidly (minutes), the movement of PCO₂ is along the blood buffer line (from N to A in the particular example in Figure 5-10), because the kidneys have not had time to affect pH. This early situation is called acute respiratory acidosis. How far up the buffer line the value moves will depend on the degree to which ventilation is insufficient to maintain PCO₂. In the example of Figure 5-10, the point has moved from the PCO₂ = 40 mm Hg isopleth to the PCO₂ = 80 mm Hg isopleth. Using Equation 4, it becomes evident that doubling PCO₂ from 40 to 80 mm Hg must have happened because either ventilation was, for some reason, cut in half while maintaining metabolic rate or metabolic rate doubled while ventilation did not change (or a combination of these two). If the acute respiratory acidosis is not treated but persists, the kidneys will start to retain HCO₃⁻, excreting acid until after a day or so, the pH, from Equation 23, is (almost) restored to normal (point C in Figure 5-10). The situation is now termed compensated respiratory acidosis. As can be seen from Figure 5-10 and the Henderson-Hasselbalch equation, doubling [HCO₃⁻] will return the ratio of [HCO₃⁻] to PCO₂ to normal, and therefore also restore pH to 7.40. In real life, renal compensation (as this process is called) is rarely complete, and so as long as PCO₂ remains elevated (in this example, at 80 mm Hg), the point labeled C will be at a lower pH and lower [HCO₃⁻] than depicted but must still lie on the isopleth for PCO₂ = 80 mm Hg.

Common clinical causes of respiratory acidosis are central nervous respiratory depression from drugs, brain injury, phrenic nerve damage, neuromuscular diseases, chest wall trauma, and lung diseases causing ventilation-perfusion inequality such as chronic obstructive pulmonary disease (COPD).

Figure 5-11 depicts the mechanism of respiratory alkalosis, which is the exact mirror image of respiratory acidosis as just described. It occurs when ventilation is increased in relation to metabolic rate, lowering both PCO₂ and lowering [HCO₃⁻], and increasing pH. Acute (point A, no renal compensation due to short duration) and fully renally compensated (C) points are indicated along with the normal (N) values. Again, complete compensation usually is not seen, so that point C is a little above and to the right of where it is shown in Figure 5-11 (but still on the same isopleth for CO₂).

A common cause of respiratory alkalosis is hyperventilation, either in intact awake persons, usually due to anxiety, or in ventilated patients, as in the ICU or during anesthesia. Additional causes are high-altitude exposure, leading to hypoxic stimulation of respiration, and lung diseases such as asthma, COPD, and interstitial pulmonary fibrosis, as evidenced by a PCO₂ lower than normal.

Figure 5-12 depicts the third type of acid-base disturbance, called metabolic acidosis. In contrast with respiratory acidosis (in which the high PCO₂ was the primary disturbance, which then led to a lower pH), metabolic acidosis achieves a low pH through generation of protons from some metabolic or external source. Referring to the Henderson-Hasselbalch equation, addition of protons must reduce [HCO₃⁻] as they combine with HCO₃⁻ to produce H₂CO₃. Although the chemoreceptors will react to the low pH rapidly (seconds), thus raising ventilation, it is useful to depict what would happen before that compensatory action takes place. In Figure 5-12, point A represents acute respiratory acidosis without change in ventilation (or, therefore, in PCO₂). The more severe the disturbance, the further down and to the left will be point A, but before ventilatory compensation, it must lie on the normal PCO₂ = 40 isopleth. Point C shows normalization of pH, achieved by hyperventilation, which lowers PCO₂ and allows pH to be restored. This is called respiratory compensation and usually is also incomplete.

In contrast with respiratory acidosis, the data point (A) lies well off (i.e., below) the normal blood buffer line, even before compensation, as Figure 5-12 shows. The vertical drop between the two essentially parallel buffer lines (in this instance, about 11 units) is termed the base deficit. It signifies how much base must be added to the blood to fully compensate for the acidosis and restore pH—in this case, 11 mmol of base/L of blood.

Common causes of metabolic acidosis include lactic acidosis (as with exercise or in multiple organ failure) and diabetic ketoacidosis.

Finally, Figure 5-13 depicts the mirror image of metabolic acidosis: metabolic alkalosis. The acute response is an increase in pH and [HCO₃⁻], from point N to A. Depression of ventilation may ensue, causing PCO₂ to rise and pH to normalize. This is a much weaker response than the converse (i.e., hyperventilation in acidosis), but if it occurs, normalization to point C results if compensation is complete.

Common causes of metabolic alkalosis are overdosing on (alkaline) antacid medications, persistent vomiting (of acid gastric fluid) secondary to a duodenal obstruction such as a scar from a previous ulcerative lesion or from cancer, and continuing use of some diuretics.

An important observation with this depiction of acid-base disturbances is that the Davenport diagrams for respiratory acidosis and metabolic alkalosis look similar after compensation—normal pH, high [HCO₃⁻], and high PCO₂. In principle, then, it is impossible to tell by which pathway the patient arrived at the compensated state, and therefore which abnormality was primary and which was the secondary, compensating process. The patient profiles usually are very different, however, and in practice, confusion is uncommon. Exactly the same issue arises for respiratory alkalosis and metabolic acidosis, and again, the clinical situations usually are very different.